Electron and kinetic energy densities for an arbitrarily closed shell in a bare Coulomb field from s-state densities

It is known from previous work that the total electron density matrix for closed-shell atoms in a bare Coulomb field is determined solely by the corresponding s-state contribution. In keeping with this philosophy, an expression is derived for the closed-shell electron density ${\rho }_n$(r) and kinetic energy density $t_n$(r) in terms only of s-state components ${\rho }_{\mathrm{no}}$(r) and $t_{\mathrm{no}}$(r) for arbitrary quantum number n. A proposal for the generalization of the present model for any central field of force is given in the Appendix.